Noncommutative K3 surfaces over finite fields get zeta functions whose point counts can be negative, obstruct geometricity, and in one explicit example, perfectly mimic a K3 surface without being geometric.
A census of cubic fourfolds over F2
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Zeta functions of K3 categories over finite fields
Noncommutative K3 surfaces over finite fields get zeta functions whose point counts can be negative, obstruct geometricity, and in one explicit example, perfectly mimic a K3 surface without being geometric.